Scott Sumner wonders what AD (aggregate demand) is, or should be

I do have a very clear idea as to what I think the profession should mean by AD—nominal GDP. And I’ve seen the AD curve drawn as a rectangular hyperbola in a few textbooks (although the number is gradually diminishing.  But it’s clear that most people don’t agree with me.  So what do they think AD is?

On some occasions people discuss AD as if it’s a real concept.  Changes in the real quantity of goods and services purchased by consumers, investors, governments, and (in net terms) foreigners.  But that can’t be AD, as it would imply that all changes in RGDP were caused by shifts in AD.  After all, all purchases are also sales, so the total aggregate quantity supplied equals the total aggregate quantity demanded.

In the textbooks AD is a downward sloping line in P/Y space, which is not generally assumed to be unit elastic.  That means when AS shifts, NGDP may also change.  But why does NGDP change? What is held constant along a given AD curve?  Presumably a given AD curve is supposed to be holding constant things like monetary and fiscal policy, animal spirits, consumer sentiment, etc.

His longer query is here.  I increasingly think it is a mistake to draw too sharp a distinction between aggregate demand and aggregate supply, at least beyond the very first round of an economic shock.  But what do you all think?  What do you all mean by “aggregate demand”?